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On partial inverse operations in the lattice of submodules
A. I. Kashu Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova
Аннотация:
In the present work two partial operations in the lattice of submodules
$\boldsymbol L(_RM)$ are defined and investigated. They are the inverse operations for
$\omega$-product and
$\alpha$-coproduct studied in [6]. This is the continuation of the article [7], in which the similar questions for the operations of
$\alpha$-product and
$\omega$-coproduct are investigated.
The partial inverse operation of
left quotient $N\,/_\odot\,K$ of
$N$ by
$K$ with respect to
$\omega$-product is introduced and similarly the
right quotient $N\,_:\backslash\,K$ of
$K$ by
$N$ with respect to
$\alpha$-coproduct is defined, where
$N,K\in\boldsymbol L(_RM)$. The criteria of existence of such quotients are indicated, as well as the different forms of representation, the main properties, the relations with lattice operations in
$\boldsymbol L(_RM)$, the conditions of cancellation and other related questions are elucidated.
Ключевые слова и фразы:
ring, module, lattice, preradical, (co)product of preradical, left (right) quotient of submodules.
MSC: 16D90,
16S90,
06B23 Поступила в редакцию: 15.05.2012
Язык публикации: английский
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